The LG-P500H most certainly has a SIM card slot and is a GSM/HSPA compatible device. The Nexus 4 takes a micro-SIM and the LG-P500H takes a mini-SIM which is larger than the microSIM. If you have the old SIM card for the LG, you may be able to reactivate it as Jonathan suggests or purchase a new SIM card.

You could get a micro to mini SIM adapter which snaps around the smaller SIM and makes it fit the bigger slot. That way you don't have to go through two extra SIMs just to swap back and forth. Use some care though - make sure the micro SIM doesn't pop out of the adapter while it's going in or out of the SIM slot, or there's a risk of damaging the SIM contacts in the older phone.